Browsing by Subject "Multilevel"
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Item Cultural stressors, internalizing symptoms, and parent-child alienation among Mexican-origin adolescents(2021-12-03) Wen, Wen, M.A.; Kim, Su YeongThe current study investigated the relation of various cultural stressors, parent-child alienation, and Mexican-origin adolescents’ internalizing symptoms at both between- and within- person levels across the course of adolescence. Positive parent-child relationships can be a critical buffer against cultural stressors for Mexican-origin adolescents. However, it is unclear whether positive parent-child relationships (i.e., low level of parent-child alienation) (1) protects against different types of cultural stressors, and (2) functions at the between- or within-person level from early to late adolescence. Method: The current study used a three-wave longitudinal dataset of 604 Mexican-origin adolescents (Wave 1: Mage = 12.41, SD = 0.97, 54% female) and conducted multilevel analysis. At the between-person level, overall low parent-child alienation buffered the adverse effects of ethnic discrimination on anxiety and the detrimental impact of cultural misfit on depressive symptoms. There were no significant within-person level interactions of parent-child alienation and cultural stressors on adolescent internalizing symptoms. The findings suggest that interventions should aim to reduce parent-child alienation throughout the course of adolescence to alleviate the impact of cultural stressors on internalizing symptoms among Mexican-origin adolescentsItem A familial longitudinal count data study(2013-05) Goren, Hakan; Powers, Daniel A.In this report, I study familial longitudinal count data with a Poisson regression model. The data is collected from individuals who are nested in families. I focus on two main issues to fit a model. The first one is the large number of excess zeros and the second one is multi-level random effects. My approach for solving these problems are to use either Zero Inflated Poisson (ZIP) or Negative Binomial (NB) models to control for the excess zeros which allow for estimation of another parameter for over dispersion while developing the model with individual and familial random effects. First, I use a Poisson regression model with only main effects. After that, I fit a ZIP model to control for the extra zeros. I provide information about general form of the exponential families and a discussion about the dispersion parameter. I also fit a Negative Binomial model instead of the ZIP model. I also build these models with only individual random effects and with both individual and familial random effects as well. I discuss the generalized estimating equation (GEE) approach to estimate the parameters of a generalized linear model with auto regressive correlation between outcomes.Item Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics(2019-08-05) Muralikrishnan, Sriramkrishnan; Bui-Thanh, Tan; Demkowicz, Leszek F; Ghattas, Omar; Raja, Laxminarayan L; Shadid, John N; Waelbroeck, Francois L; Wheeler, Mary FThe hybridized discontinuous Galerkin methods (HDG) introduced a decade ago is a promising candidate for high-order spatial discretization combined with implicit/implicit-explicit time stepping. Roughly speaking, HDG methods combines the advantages of both discontinuous Galerkin (DG) methods and hybridized methods. In particular, it enjoys the benefits of equal order spaces, upwinding and ability to handle large gradients of DG methods as well as the smaller globally coupled linear system, adaptivity, and multinumeric capabilities of hybridized methods. However, the main bottleneck in HDG methods, limiting its use to small to moderate sized problems, is the lack of scalable linear solvers. In this thesis we develop fast and scalable solvers for HDG methods consisting of domain decomposition, multigrid and multilevel solvers/preconditioners with an ultimate focus on simulating large scale problems in fluid dynamics and magnetohydrodynamics (MHD). First, we propose a domain decomposition based solver namely iterative HDG for partial differential equations (PDEs). It is a fixed point iterative scheme, with each iteration consisting only of element-by-element and face-by-face embarrassingly parallel solves. Using energy analysis we prove the convergence of the schemes for scalar and system of hyperbolic PDEs and verify the results numerically. We then propose a novel geometric multigrid approach for HDG methods based on fine scale Dirichlet-to-Neumann maps. The algorithm combines the robustness of algebraic multigrid methods due to operator dependent intergrid transfer operators and at the same time has fixed coarse grid construction costs due to its geometric nature. For diffusion dominated PDEs such as the Poisson and the Stokes equations the algorithm gives almost perfect hp--scalability. Next, we propose a multilevel algorithm by combining the concepts of nested dissection, a fill-in reducing ordering strategy, variational structure and high-order properties of HDG, and domain decomposition. Thanks to its root in direct solver strategy the performance of the solver is almost independent of the nature of the PDEs and mostly depends on the smoothness of the solution. We demonstrate this numerically with several prototypical PDEs. Finally, we propose a block preconditioning strategy for HDG applied to incompressible visco-resistive MHD. We use a least squares commutator approximation for the inverse of the Schur complement and algebraic multigrid or the multilevel preconditioner for the approximate inverse of the nodal block. With several 2D and 3D transient examples we demonstrate the robustness and parallel scalability of the block preconditioner